Primary 5 Mathematics Semestral Assessment 2 (End of Year) Paper 5

TuitionGoWhere Practice Paper - Mathematics Primary 5 (SA2 Version 5) - Answer Key

Total Marks: 80

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SECTION A: Multiple-Choice Questions (20 marks)

1. Answer: (2) 200 000 [2]

Working:
The number is 7 248 391.
Place values: 7 (millions), 2 (hundred thousands), 4 (ten thousands), 8 (thousands), 3 (hundreds), 9 (tens), 1 (ones).
Digit 2 is in the hundred thousands place → 2 × 100 000 = 200 000.

Key concept: In a 7-digit number, the place values from left to right are: millions, hundred thousands, ten thousands, thousands, hundreds, tens, ones.

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2. Answer: (2) 4 590 000 [2]

Working:
Number: 4 587 632
Ten thousands digit = 8
Next digit (thousands) = 7 ≥ 5, so round up the ten thousands digit from 8 to 9.
4 587 632 → 4 590 000

Key concept: When rounding to the nearest ten thousand, look at the thousands digit. If ≥ 5, round up; if < 5, round down.

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3. Answer: (1) 6 345 298 [2]

Working:
6 000 000 + 300 000 = 6 300 000
6 300 000 + 40 000 = 6 340 000
6 340 000 + 5 000 = 6 345 000
6 345 000 + 200 = 6 345 200
6 345 200 + 90 = 6 345 290
6 345 290 + 8 = 6 345 298

Key concept: Add each place value component systematically.

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4. Answer: (1) 5 654 322 [2]

Working:
8 000 000 − 2 345 678
= 5 654 322

Check: 5 654 322 + 2 345 678 = 8 000 000 ✓

Key concept: Subtraction with regrouping across zeros. Verify by adding back.

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5. Answer: (1) 1 358 400 [2]

Working:
4 528 × 300 = 4 528 × 3 × 100
= 13 584 × 100
= 1 358 400

Key concept: Multiply by multiples of 10, 100, 1000 by multiplying by the non-zero digit first, then adding zeros.

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6. Answer: (2) 90 000 [2]

Working:
7 200 000 ÷ 800 = 7 200 000 ÷ (8 × 100)
= (7 200 000 ÷ 100) ÷ 8
= 72 000 ÷ 8
= 9 000

Wait, let me recalculate:
7 200 000 ÷ 800 = 72 000 ÷ 8 = 9 000? No.
7 200 000 ÷ 800 = 7 200 000 ÷ 800
= 72 000 ÷ 8 (dividing numerator and denominator by 100)
= 9 000

But 9 000 × 800 = 7 200 000 ✓
So answer is 9 000, which is option (1).

Correction: Answer: (1) 9 000 [2]

Working:
7 200 000 ÷ 800 = 72 000 ÷ 8 = 9 000

Key concept: Cancel zeros when dividing by multiples of 10, 100, 1000.

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7. Answer: (2) 111 [2]

Working:
45 + 12 × 6 − 18 ÷ 3
Order of operations: × and ÷ before + and −
= 45 + 72 − 6
= 117 − 6
= 111

Key concept: BODMAS/BIDMAS - Brackets, Orders, Division/Multiplication (left to right), Addition/Subtraction (left to right).

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8. Answer: (1) 1 500 [2]

Working:
(5 400 + 600) ÷ 20 × 5
= 6 000 ÷ 20 × 5
= 300 × 5
= 1 500

Key concept: Brackets first, then division and multiplication from left to right.

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9. Answer: (1) 25 350 [2]

Working:
January: 8 450 toys
February: 3 × 8 450 = 25 350 toys

Key concept: "3 times as many" means multiply by 3.

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10. Answer: (1) $5 400 [2]

Working:
Total money = $12 000 Spent on TV =$\frac{2}{5} \times 12 000 = $4 800 Remainder =$12 000 − $4 800 =$7 200
Spent on refrigerator = $\frac{1}{4} \times 7 200 =$1 800
Left = $7 200 −$1 800 = $5 400

Key concept: "Fraction of remainder" means the denominator applies to the remaining amount after the first spending.

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SECTION B: Short-Answer Questions (25 marks)

11. Answer: Nine million forty thousand five hundred six [1]

Explanation:
9 040 506 = 9 000 000 + 40 000 + 500 + 6
Read in groups of three digits from right: 9 (million), 040 (thousand), 506
→ Nine million forty thousand five hundred six

Note: Do not say "and" between place values in Singapore math convention. "Zero" in ten thousands and thousands places is not read aloud.

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12. Answer: 700 000 [1]

Explanation:
Number: 5 782 341
Place values: 5 (millions), 7 (hundred thousands), 8 (ten thousands), 2 (thousands), 3 (hundreds), 4 (tens), 1 (ones)
Digit 7 is in the hundred thousands place → 7 × 100 000 = 700 000

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13. Answer: 4 208 500, 4 280 500, 4 802 500, 4 820 500 [2]

Working:
Compare digits from left to right (millions → hundred thousands → ten thousands → thousands):
All have 4 millions.
Hundred thousands: 2, 2, 8, 8 → 2 < 8
For the two with 2 hundred thousands: ten thousands are 0 and 8 → 0 < 8 → 4 208 500 < 4 280 500
For the two with 8 hundred thousands: ten thousands are 0 and 2 → 0 < 2 → 4 802 500 < 4 820 500
Order: 4 208 500 < 4 280 500 < 4 802 500 < 4 820 500

Key concept: Compare numbers digit by digit from the highest place value.

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14. Answer: 268 200 [2]

Working:
6 705 × 40 = 6 705 × 4 × 10
= 26 820 × 10
= 268 200

Check: 6 705 × 4 = 26 820, then × 10 = 268 200 ✓

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15. Answer: 16 460 [2]

Working:
9 876 000 ÷ 600 = 9 876 000 ÷ (6 × 100)
= (9 876 000 ÷ 100) ÷ 6
= 98 760 ÷ 6
= 16 460

Check: 16 460 × 600 = 16 460 × 6 × 100 = 98 760 × 100 = 9 876 000 ✓

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16. Answer: 196 000 [2]

Working:
Round 4 892 to nearest ten → 4 890
Round 39 to nearest ten → 40
Estimated product = 4 890 × 40
= 4 890 × 4 × 10
= 19 560 × 10
= 195 600 ≈ 196 000 (to nearest thousand, or keep as 195 600)

Note: The question asks to estimate by rounding each to nearest ten, so 4 890 × 40 = 195 600. Accept 195 600 or 196 000.

Key concept: Estimation by rounding makes mental calculation easier. Round each factor first, then multiply.

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17. Answer: 1 380 [2]

Working:
7 200 ÷ (50 − 10) × 6 + 300
= 7 200 ÷ 40 × 6 + 300 (brackets first)
= 180 × 6 + 300 (division before multiplication, left to right)
= 1 080 + 300
= 1 380

Key concept: BODMAS - Brackets, then Division/Multiplication left to right, then Addition/Subtraction.

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18. Answer: 85 018 [2]

Working:
Number = (Divisor × Quotient) + Remainder
= (25 × 3 400) + 18
= 85 000 + 18
= 85 018

Check: 85 018 ÷ 25 = 3 400 remainder 18 ✓

Key concept: Division algorithm: Dividend = Divisor × Quotient + Remainder.

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19. Answer: 60 [2]

Working:
Total apples = 15 × 24 = 360
Number of bags = 360 ÷ 6 = 60

Alternative: 24 ÷ 6 = 4 bags per box, 15 × 4 = 60 bags.

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20. Answer: 3 650 [3]

Working:
Let the two numbers be $x$ (larger) and $y$ (smaller).
$x + y = 8 500$
$x - y = 1 200$

Add the two equations:
$2x = 9 700$
$x = 4 850$

$y = 8 500 - 4 850 = 3 650$

Alternative (model method):
Sum = 8 500, Difference = 1 200
Smaller number = (Sum − Difference) ÷ 2 = (8 500 − 1 200) ÷ 2 = 7 300 ÷ 2 = 3 650

Marking:

• Correct method: 1 mark
• Correct working: 1 mark
• Correct answer: 1 mark

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SECTION C: Structured / Long-Answer Questions (35 marks)

21. [3]

(a) Answer: 6 900 [1]
Working:
Chinese books = English books + 2 340 = 4 560 + 2 340 = 6 900

(b) Answer: 5 730 [1]
Working:
Total English + Chinese = 4 560 + 6 900 = 11 460
Malay books = $\frac{1}{2} \times 11 460 = 5 730$

(c) Answer: 17 190 [1]
Working:
Total books = 4 560 + 6 900 + 5 730 = 17 190

Marking: 1 mark each for correct answers with working shown.

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22. [4]

(a) Answer: $\frac{1}{4}$ [1]
Working:
Fraction spent on watch = $\frac{3}{8}$
Remainder = $1 - \frac{3}{8} = \frac{5}{8}$
Fraction spent on belt = $\frac{2}{5} \times \frac{5}{8} = \frac{10}{40} = \frac{1}{4}$

**(b) Answer: $3 360 [3]** **Working:** Total fraction spent =$\frac{3}{8} + \frac{1}{4} = \frac{3}{8} + \frac{2}{8} = \frac{5}{8}$Fraction left =$1 - \frac{5}{8} = \frac{3}{8}$$\frac{3}{8}$of money =$1 260
$\frac{1}{8}$ of money = $1 260 ÷ 3 =$420
Total money = $420 × 8 =$3 360

Check:
Watch: $\frac{3}{8} \times 3 360 =$1 260
Remainder: $3 360 -$1 260 = $2 100 Belt:$\frac{2}{5} \times 2 100 = $840 Left:$2 100 - $840 =$1 260 ✓

Marking:

• (a) Correct fraction with working: 1 mark
• (b) Correct method (fraction left or model): 1 mark
• (b) Correct unit value calculation: 1 mark
• (b) Correct final answer: 1 mark

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23. [4]

(a) Answer: 2 500 [1]
Working:
Toys per day = 12 500 ÷ 5 = 2 500

**(b) Answer: $100 000 [3]** **Working:** Total toys in 5 days = 12 500 Total money = 12 500 ×$8 = $100 000

Alternative: Daily collection = 2 500 × $8 =$20 000, 5 days = $20 000 × 5 =$100 000

Marking:

• (a) Correct division: 1 mark
• (b) Correct multiplication set-up: 1 mark
• (b) Correct working: 1 mark
• (b) Correct answer with unit: 1 mark

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24. [5]

(a) Answer: 800 [1]
Working:
Lower primary = $\frac{2}{9} \times 3 600 = 800$

(b) Answer: 1 000 [2]
Working:
Remaining after lower primary = 3 600 − 800 = 2 800
Middle primary = $\frac{5}{12} \times 2 800 = 1 166.66...$

Wait, 2 800 ÷ 12 = 233.33, × 5 = 1 166.67. This doesn't give a whole number. Let me recheck.

$\frac{5}{12} \times 2 800 = \frac{14 000}{12} = 1 166 \frac{2}{3}$

This is problematic for a P5 question. Let me adjust the numbers mentally... Actually, the question as written gives a non-integer. In a real exam, numbers would be chosen to give whole numbers. Let me recalculate with the given numbers and note the issue.

Actually, 3 600 × $\frac{2}{9}$ = 800 exactly.
Remaining = 2 800.
$\frac{5}{12} \times 2 800 = 1 166 \frac{2}{3}$ - not a whole number of pupils.

This suggests the question has a flaw. But as an answer key, I'll show the mathematical working and note the issue.

Revised working for (b) and (c) with exact fractions:
Middle primary = $\frac{5}{12} \times 2 800 = \frac{14 000}{12} = 1 166 \frac{2}{3}$
Upper primary = 2 800 − 1 166 $\frac{2}{3}$ = 1 633 $\frac{1}{3}$
Difference (upper - lower) = 1 633 $\frac{1}{3}$ − 800 = 833 $\frac{1}{3}$

But pupils must be whole numbers. In a real paper, the total would be a multiple of 36 (LCM of 9 and 12). Let's assume the question intended 3 600 to work... Actually 3 600 ÷ 9 = 400, × 2 = 800. Remaining 2 800. 2 800 ÷ 12 = 233.33. Not divisible by 12.

Correction for answer key: I'll present the exact fractional working and note that in a real exam, numbers would be chosen to give whole numbers. But since this is the generated question, I'll provide the mathematical answers.

Actually, let me re-read the question: "There are 3 600 pupils in a school. $\frac{2}{9}$ of the pupils are in the lower primary. $\frac{5}{12}$ of the remaining pupils are in the middle primary. The rest are in the upper primary."

This is a standard "fraction of remainder" problem. The numbers should work out. 3 600 is divisible by 9 (400). Remainder 2 800. For $\frac{5}{12}$ of 2 800 to be whole, 2 800 must be divisible by 12. 2 800 ÷ 12 = 233.33. Not divisible.

Decision: I'll provide the exact fractional answers and add a note. In practice, the question would use 3 600 → change to 3 600? No, 3 600 is given. Let me check: maybe it's $\frac{5}{14}$? No, template says $\frac{5}{12}$.

I'll proceed with exact values and note the anomaly.

(b) Answer: 1 166 $\frac{2}{3}$ (or 1 167 if rounding, but mathematically 1 166 $\frac{2}{3}$) [2]
Working:
Remaining pupils = 3 600 − 800 = 2 800
Middle primary = $\frac{5}{12} \times 2 800 = \frac{14 000}{12} = 1 166 \frac{2}{3}$

(c) Answer: 833 $\frac{1}{3}$ [2]
Working:
Upper primary = 2 800 − 1 166 $\frac{2}{3}$ = 1 633 $\frac{1}{3}$
Difference = Upper − Lower = 1 633 $\frac{1}{3}$ − 800 = 833 $\frac{1}{3}$

Note: In an actual examination, the total number of pupils would be chosen such that all fractions yield whole numbers (e.g., 3 600 is divisible by 9 but the remainder 2 800 is not divisible by 12). A better total would be 3 600 → 3 600 is actually 36 × 100. LCM of 9 and 12 is 36. 3 600 ÷ 36 = 100. So it should work! Let me recheck: $\frac{2}{9} = \frac{8}{36}$. Remainder = $\frac{28}{36} = \frac{7}{9}$. $\frac{5}{12} = \frac{15}{36}$. $\frac{15}{36}$ of total = $\frac{15}{36} \times 3 600 = 1 500$. Ah! "of the remaining pupils" - so it's $\frac{5}{12}$ of remainder, not $\frac{5}{12}$ of total.

Remainder = $\frac{7}{9} \times 3 600 = 2 800$.
$\frac{5}{12} \times 2 800 = \frac{5}{12} \times \frac{7}{9} \times 3 600 = \frac{35}{108} \times 3 600 = 35 \times 33.33...$ = 1 166.67. Still not whole.

For it to be whole, total must be multiple of 108. 3 600 ÷ 108 = 33.33. Not a multiple.

Conclusion: The question as generated has a numerical flaw. I'll provide the exact fractional answers.

Marking (adjusted for fractional answers):

• (a) Correct: 1 mark
• (b) Correct method (remainder × fraction): 1 mark, correct value: 1 mark
• (c) Correct method (upper = remainder - middle, difference = upper - lower): 1 mark, correct value: 1 mark

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25. [7]

(a) Answer: 100 000 cm³ [2]
Working:
Volume of water = length × breadth × height of water
= 80 cm × 50 cm × 25 cm
= 100 000 cm³

(b) Answer: 60 litres [2]
Working:
Total tank volume = 80 × 50 × 40 = 160 000 cm³
Volume of water = 100 000 cm³
Empty volume = 160 000 − 100 000 = 60 000 cm³
Litres needed = 60 000 ÷ 1 000 = 60 litres

(c) Answer: 30 minutes [3]
Working:
Water needed = 60 litres
Rate = 2 litres per minute
Time = 60 ÷ 2 = 30 minutes

Marking:

• (a) Correct formula and substitution: 1 mark, correct answer with unit: 1 mark
• (b) Correct total volume: 1 mark, correct conversion to litres: 1 mark
• (c) Correct division: 1 mark, correct unit (minutes): 1 mark, correct answer: 1 mark

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MARKING SUMMARY

Section	Questions	Marks
A (MCQ)	1-10	20
B (Short Answer)	11-20	25
C (Structured)	21-25	35
Total	25	80

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COMMON MISTAKES TO AVOID

1. Place value errors: Confusing hundred thousands with millions, or misreading zeros in large numbers.
2. Rounding: Forgetting to look at the next digit, or rounding the wrong place value.
3. Order of operations: Doing addition before multiplication/division, or not working left-to-right for same-precedence operations.
4. Fraction of remainder: Applying the second fraction to the original amount instead of the remainder.
5. Unit conversion: Forgetting to convert cm³ to litres (÷ 1000) or vice versa.
6. Estimation: Rounding after multiplying instead of before, or rounding to wrong place value.
7. Division with remainder: Forgetting to add the remainder back when reconstructing the original number.

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END OF ANSWER KEY